Constructs planar diagram models for noncrossing partitions in affine Coxeter groups of types à and C̃, completing [1,c]_T to a lattice with diagram-guided factorizations.
Noncrossing partitions of a marked surface
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures.
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UNVERDICTED 2representative citing papers
Models the interval [1,c]_T in the absolute order for affine Coxeter groups of types tilde D and tilde B by symmetric noncrossing partitions of an annulus with one or two double points, also covering a larger lattice in type tilde B.
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Noncrossing partitions of an annulus
Constructs planar diagram models for noncrossing partitions in affine Coxeter groups of types à and C̃, completing [1,c]_T to a lattice with diagram-guided factorizations.
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Symmetric noncrossing partitions of an annulus with double points
Models the interval [1,c]_T in the absolute order for affine Coxeter groups of types tilde D and tilde B by symmetric noncrossing partitions of an annulus with one or two double points, also covering a larger lattice in type tilde B.